$ν$SpaceSim: A Comprehensive Simulation Package for Modeling the Measurement of Cosmic Neutrinos using the Earth as the Neutrino Target and Space-based Detectors

$ν$SpaceSim is a highly-efficient (e.g., fast) module-based, end-to-end simulation package that models the physical processes of cosmic neutrino interactions that leads to detectable signals for sub-orbital and space-based instruments. Starting with an input flux of neutrinos incident on a user-specified geometry in the Earth, the flux of Earth-emergent leptons are calculated followed by their subsequent extensive air showers (EAS). Next, the EAS optical Cherenkov and radio emission, signal attenuation to the detector, and the detector response are modeled to determine the sensitivity to both the diffuse cosmic neutrinos and transient neutrino sources. Using the Earth as a tau neutrino target and the atmosphere as the signal generator effectively forms a detector with a mega-gigaton mass. Furthermore, \taon decays and neutrino neutral-current interactions within the Earth (re)generates a flux of lower energy tau neutrinos that can also interact in the Earth thus enhancing the detection probability. $ν$SpaceSim provides a tool to both understand the data from recent experiments such as EUSO-SPB2 as well as design/understand the performance the next generation of balloon- and space-based experiments, including POEMMA Balloon with Radio (PBR) and the Payload for Ultrahigh Energy Observations (PUEO). In this paper the $ν$SpaceSim software, physics modeling, and the cosmic neutrino measurement capabilities of example sub-orbital and space-based experimental configurations are presented as well as status of planned modeling upgrades.